The problem states Theorem 1.7, the Tietze Extension Theorem. The theorem states that if $(X, \tau)$ is a normal space, and $F$ is a closed subspace of $X$, and $f: F \rightarrow [a, b]$ is a continuous function, then $f$ has an extension $h$ over $X$ with values in $[a, b]$. The text then indicates that in the proof, one can assume that $a = -1$ and $b = 1$.

1. Problem Description

The problem states Theorem 1.7, the Tietze Extension Theorem. The theorem states that if $(X, \tau)$ is a normal space, and $F$ is a closed subspace of $X$, and $f: F \rightarrow [a, b]$ is a continuous function, then $f$ has an extension $h$ over $X$ with values in $[a, b]$. The text then indicates that in the proof, one can assume that $a = -1$ and $b = 1$.

2. Solution Steps

The problem does not ask to solve anything. It just states the Tietze Extension Theorem.

The Tietze Extension Theorem states that for a normal space $X$, any continuous function $f: F \rightarrow [a,b]$ defined on a closed subset $F$ of $X$ can be extended to a continuous function $h: X \rightarrow [a,b]$.

The problem doesn't require a specific solution since it is simply stating a theorem. The next line says that in the proof, it suffices to consider the case where the interval is $[-1, 1]$.

3. Final Answer

The problem only states the Tietze Extension Theorem. No specific solution is needed.